Question:
The number of solutions of the equation \( \tan x + \sec x = 2 \cos x \) lying in the interval \( [0, 2\pi] \) is
The number of solutions of the equation \( \tan x + \sec x = 2 \cos x \) lying in the interval \( [0, 2\pi] \) is
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When solving trigonometric equations, try using standard identities and simplify the equation before solving for the variable.
Updated On: Jan 27, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Simplify the given equation.
The given equation is \( \tan x + \sec x = 2 \cos x \). Rewriting the trigonometric functions, we get: \[ \frac{\sin x}{\cos x} + \frac{1}{\cos x} = 2 \cos x \]
Step 2: Solve for \( x \).
Multiply through by \( \cos x \) to clear the denominators: \[ \sin x + 1 = 2 \cos^2 x \] Using the identity \( \cos^2 x = 1 - \sin^2 x \), substitute and solve for the values of \( x \) in the interval \( [0, 2\pi] \).
Step 3: Conclusion.
The correct number of solutions is 2.
The given equation is \( \tan x + \sec x = 2 \cos x \). Rewriting the trigonometric functions, we get: \[ \frac{\sin x}{\cos x} + \frac{1}{\cos x} = 2 \cos x \]
Step 2: Solve for \( x \).
Multiply through by \( \cos x \) to clear the denominators: \[ \sin x + 1 = 2 \cos^2 x \] Using the identity \( \cos^2 x = 1 - \sin^2 x \), substitute and solve for the values of \( x \) in the interval \( [0, 2\pi] \).
Step 3: Conclusion.
The correct number of solutions is 2.
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